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Dimeric Molecular Association of Dimethyl Sulfoxide in Solutions of Nonpolar Liquids Toshiyuki Shikata* and Natsuki Sugimoto Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560-0043, Japan ABSTRACT: Although many vibrational spectroscopic studies using infrared (IR) absorption and Raman scattering (RS) techniques revealed that dimethyl sulfoxide (DMSO) forms intermolecular dimeric associations in the pure liquid state and in solutions, the results of a number of dielectric relaxation studies did not clearly show the presence of such dimers. Recently, we found the presence of dimeric DMSO associations in not only the pure liquid but also in solutions of nonpolar solvents, such as tetrachloromethane (CCl4) and benzene (Bz), using dielectric relaxation (DR) techniques, which ranged from 50 MHz to 50 GHz at 25 °C. The dimeric DMSO associations cause a slow dielectric relaxation process with a relaxation time of ca. 23 ps for solutions in CCl4 (ca. 17 ps in Bz) due to the dissociation into monomeric DMSO molecules, while the other fast relaxation is caused by monomeric DMSO molecules with a relaxation time of ca. 5.0 ps (ca. 5.5 ps in Bz) at 25 °C. A comparison of DR and vibrational spectroscopic data for DMSO solutions demonstrated that the concentration dependence of the relative magnitude of the slow and fast DR strength corresponds well to the two IR and RS bands assigned to the vibrational stretching modes of the sulfoxide groups (SdO) of the dimeric associations and the monomeric DMSO molecules, respectively. Moreover, the concentrations of the dimeric associations ([DIM]) and monomeric DMSO molecules ([MON]) were governed by a chemical equilibrium and an equilibrium constant (Kd = [DIM]2[MON]1) that was markedly dependent on the concentration of DMSO and the solvent species (Kd = 2.5 ( 0.5 M1 and 0.7 ( 0.1 M1 in dilute CCl4 and Bz solutions, respectively, and dramatically increased to 2040 M1 in pure DMSO at 25 °C).
’ INTRODUCTION Dimethyl sulfoxide, DMSO, is one of the typical dipolar aprotic molecules possessing an extremely large dipole moment of ca. 3.95 D and is widely used as a solvent in many types of chemical reactions that require high polarity as well as in analytical methods and practical applications in biochemistry and pharmacology.1,2 DMSO occasionally exhibits strongly nonideal, anomalous physicochemical behaviors.1 An important reason for its anomalous behaviors is its tendency to form intermolecular associations with itself and with other molecules, such as water. Infrared (IR) absorption and Raman scattering (RS) techniques have been used to investigate the structures of DMSO in the pure liquid state and in solution in a wavenumber range from 900 to 1100 cm1.38 Figueroa et al.3 first reported that the self-association of DMSO in dilute tetrachloromethane (CCl4) solutions is limited to the formation of dimers, which have an equilibrium constant of Kd = 0.9 M1 at 25 °C, and they proposed an antiparallel cyclic configuration for the molecular dimers based on the results from IR experiments. They assigned the IR bands found at 1060 and 1000 cm1 to the vibrational stretching bands of the sulfoxide (SdO) groups of monomeric DMSO molecules and to dimeric molecular associations, respectively. However, it has been shown that their estimation of Kd is incorrect due to erroneous assignments of the vibrational stretching band for the SdO groups at 1000 cm1 for the dimeric r 2011 American Chemical Society
DMSO association.47 Fawcett et al.5 accounted for the error in the band assignment and reported a more reliable Kd value (0.22 M1) for DMSO solutions in a polar solvent (acetonitrile), which was based on experimental results from an attenuated total reflection (ATR) IR absorption technique and showed that the vibration stretching band for the SdO groups of the dimeric DMSO association remained at 1044 cm1 irrespective of the DMSO concentration. This assignment has been widely accepted as correct.4 Fawcett et al.5 also concluded that the dimeric DMSO association possesses a cyclic antiparallel configuration, as proposed by Figueroa et al.3 A number of RS experiments have also revealed the presence of dimeric associations and/or larger associations in the pure liquid state and in solutions.49 Using RS techniques, Perelygin et al.10 investigated the molecular association of DMSO in the pure liquid state and in solutions. They proposed the coexistence of both the antiparallel cyclic and parallel chainlike associations for DMSO. The vibrational band observed at 1027 cm1 was attributed to the SdO stretching vibration of DMSO molecules in the parallel chainlike molecular associations, and the bands observed at 1058 and 1044 cm1 were attributed to the out-of-phase Received: October 21, 2011 Revised: November 20, 2011 Published: December 19, 2011 990
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The Journal of Physical Chemistry A and in-phase SdO stretching vibration modes, respectively, in the antiparallel cyclic associations.10 However, these assignments have not yet been accepted as correct.5,9 If the cyclic antiparallel dimer has an inversion center, then the two bands due to the SdO stretching vibrations are the symmetric, in-phase stretching RSactive vibration band and the asymmetric, out-of-phase IR active band.5,6,8 In the RS spectra of DMSO in the pure liquid state, the in-phase SdO stretching vibration for the dimeric association was observed at 1042 cm1, while in the IR spectra, the corresponding out-of-phase vibration band was observed at 1044 cm1.5 The reason for this small splitting between the two bands for the SdO stretching vibrations has been assigned to the absence of rigorous symmetry in the structure of the cyclic dimer.5 However, Skripkin et al.9 recently proposed that the out-of-phase stretching vibration band of the cyclic dimer is observed at 1063 cm1 in the IR spectra. Moreover, if the cyclic dimer has distorted symmetry without an inversion center, the two SdO stretching bands expected in the RS spectra are the in-phase band, which is observed at 1042 cm1 as described above, and the not-in-phase and IR-active band.5 Furthermore, it is well-known that the four distinct rocking vibration modes of the methyl groups in DMSO are observed at ca. 895, 930, 950, and 1020 cm1, irrespective of the formation of the dimeric molecular association, and the magnitude of these modes are proportional to the concentration of monomeric DMSO in the solution. However, published IR and RS experimental spectra for pure DMSO and its solutions have been significantly dependent on the DMSO samples used by each research group even under the same conditions, especially for the pure liquid state of DMSO. It appears that the water content remaining in the DMSO as an impurity is not perfectly controlled in some of the studies. The correct assignment of each vibrational band for DMSO in the pure liquid state and in solution is necessary and requires that the sample solutions be prepared with completely dehydrated pure DMSO. X-ray11 and neutron-diffraction experiments12 on DMSO in the pure liquid state coupled with empirical potential-structurerefinement modeling, Monte Carlo simulations combined with ab initio quantum chemical calculations,13 and molecular-dynamics simulations (MD)1,2,1214 have revealed that neighboring DMSO molecules are aligned in an antiparallel configuration due to the strong dipoledipole interactions between the SdO groups. These results strongly suggest that DMSO has an obvious tendency to form dimers in an antiparallel configuration in both the pure liquid state and in solution. The crystalline structure of DMSO consists of arrangements of dimeric associations in an antiparallel configuration15 over a wide pressure range, which also strongly supports the presence of antiparallel dimers in the pure liquid state. Consequently, most structural investigations support the presence of antiparallel cyclic dimers. However, the results from numerous dielectric relaxation (DR) studies did not support the presence of intermolecular associations because the obtained Kirkwood correlation factor (gK), which was very close to unity, and the magnitude of the orientational correlation between the dipoles of each DMSO molecule indicated free rotation of DMSO molecules in the pure liquid state1618 and in solution.19 The reported gK values are close to unity because the high frequency limiting permittivity (ε∞), which is necessary for the calculation of gK, was not correctly determined due to technical reasons. The expression ε∞ = 1.1n2, where n is the refractive index of the sample, has been used in many dielectric studies because of the difficulty of performing DR experiments at sufficiently high frequencies for the precise determination of ε∞.1619 This simple but vague approximation
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for ε∞ leads to gK values close to unity for DMSO in both the pure liquid state and in solution even when DR experiments are performed at low frequencies to determine the static dielectric constant, ε0. Thus, it is important to determine precise ε∞ values from experiments over a sufficiently high frequency range for the correct determination of gK. Recently, we have confirmed that the ε∞ value of DMSO determined from DR measurements in a high-frequency range up to 50 GHz is not expressed well by the relationship ε∞ = 1.1n2 in the pure liquid state but that it is approximately twice as large as that predicted by this relationship.20 The temperature dependence of the experimentally determined real and imaginary parts of the electric permittivity (ε0 and ε00 ) and the ε∞ values revealed that DMSO molecules form dimeric associations with an antiparallel configuration and that the dimeric association process is governed by a chemical equilibrium with an equilibrium constant that is highly dependent on temperature.20 Consequently, accurate DR measurements in a sufficiently high-frequency range would permit one to determine the equilibrium constants of the dimeric association process of DMSO in solution similar to the process for vibrational spectroscopic methods, such as IR and RS techniques. In this study, we performed IR and RS measurements in two types of DMSO solutions including tetrachloromethane (CCl4) and benzene (Bz) to determine the exact equilibrium constants of the dimerization process of DMSO in each solution as a function of the concentration of DMSO using a conventional analysis of the relationship between the IR absorbance (and Raman scattering intensities) of monomeric DMSO molecules and dimeric associations.5 In previous studies5 that determined the equilibrium constants of the dimeric process in DMSO solutions at constant temperatures using IR techniques, the equilibrium constants were assumed to be independent of the concentration of DMSO. However, there is no logical or realistic reason for this assumption. The concentration dependence of the equilibrium constants of the dimeric process in the solutions determined using DR techniques were compared with those obtained from IR and RS techniques. The validity of the evaluation method for the dimeric equilibrium constants using DR techniques will be discussed.
’ EXPERIMENTAL SECTION Materials. Highly dehydrated DMSO (purity >99% and certified water content 99%) were also purchased from Wako Pure Chemical Industries and were used as solvents for the preparation of the DMSO solutions. DMSO concentrations in both the DMSO/CCl4 and DMSO/Bz solutions ranged from c = 0.04 to 14.08 M (in the pure liquid state). Methods. The IR spectra of both the DMSO/CCl4 and DMSO/Bz solutions were recorded with a Bio-Rad Excalibur FTS 3000 (Fourier Transform IR spectrometer: Bio-Rad, Varian, Agilent Technologies, Santa Clara) equipped with a sandwich-type 991
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liquid cell constructed using two calcium fluoride (CaF2) crystalline window plates with a diameter of 20 mm and a thickness of 2 mm separated by two types of spacer sheets with a thickness of ca. 0.01 and 0.02 mm. The thickness of the liquid samples was adequately modified via the appropriate choice of a spacer plate for each sample to produce high-quality absorption spectra for quantitative analysis. All of the IR measurements were performed at room temperature, ca. 25 °C. KBr crystalline plates were not used in the IR experiments because water molecules adsorbed on the surface of the crystals dissolved into the samples and crucially affected obtained spectra. RS spectra for the DMSO/CCl4 solution were recorded on an NR1800 (Micro-Raman Spectrometer, JASCO, Tokyo) equipped with argon-ion, Ar+, laser at 514.5 nm. All of the RS measurements were performed at room temperature, ca. 25 °C. A dielectric-probe kit (8507E, Agilent Technologies, Santa Clara) equipped with a PNA-L network analyzer (N5230C, Agilent Technologies) and a performance probe for 50 GHz was employed to measure ε0 and ε00 over a frequency range of 50 MHz to 50 GHz. A three-load calibration procedure with three liquids (n-hexane, 3-pentanone, and water) was performed at 25 °C prior to the dielectric measurements of sample solutions. The electric permittivity of n-hexane at 25 °C was quoted from the literature.21 To test the accuracy of the system, we measured the dielectric spectra of the two solvents, CCl4 and Bz, at 25 °C prior to measurements of DMSO and its solutions. ε0 = 2.25 ( 0.01 and ε00 = 0.00 ( 0.05 and ε0 = 2.29 ( 0.03 and ε00 = 0.00 ( 0.05 were obtained for CCl4 and Bz, respectively, with no dielectric dispersion irrespective of the frequency (ω) when ω > 3 109 s1. These dielectric constants, ε0 (ε0 ) for CCl4 and Bz, are in agreement with the values of ca. 2.23 and 2.27 reported in the literature.19,22 From these, the measuring system performed the dielectric relaxation measurements for DMSO in the pure liquid state and in solution with an uncertainty of less than 2.0% in the range of ω > 109 s1. The temperature of the sample liquids was adjusted to T = 25 °C with an accuracy of (0.1 °C using a temperature-control system equipped with a Peltier device.
concentration of DMSO (c) in the DMSO/CCl4 solutions. An interesting aspect of these spectra is that the shape of the IR adsorption and the RS intensity in the range of 10001080 cm1 is significantly altered, and the peak wavenumbers change from ca. 1045 to 1065 cm1 as the c decreases, which directly corresponds to the change in composition of the monomeric DMSO molecules and antiparallel cyclic dimers. This result is discussed in more detail later. Another interesting aspect observed in Figure 1 is that the vibrational modes observed at 1020 and 930 cm1 in the IR spectra are much less significant in the RS spectra, irrespective of the c value. This result implies that the bands are not inert in the RS, whereas the RS sensitivity (susceptibility) of these vibrational bands is much lower than for the band at 950 cm1. According to previous studies,4,6 DMSO has four types of methyl-rocking modes (ca. 895, 930, 950, and 1020 cm1 in the pure liquid state). All of the rocking modes are active in both the IR and RS spectra without changing its shape like splitting into two new modes depending on the concentration, c, of DMSO. Therefore, the magnitudes of the IR absorption and the RS intensity for these rocking modes should be proportional to c, while wavenumbers of the modes depend slightly on c. Fawcett et al.5 accepted the assignment of the vibrational modes for DMSO provided by Forel et al.4 and concluded that the vibrational band at 1020 cm1 is a methyl rocking mode with the direction of the vibration parallel to the CSC plane and the in-phase methyl stretching (F||(CH3)A0 ). All of the IR absorption and RS intensity spectra in the range of 9501100 cm1 were decomposed into Lorentz function-type constituent modes via a curve fit procedure. Parts a and b of Figure 2 show the typical results from the decomposition of the spectra for DMSO in the pure liquid state (c = 14.08 M). The total summation of the constituent Lorentz functions perfectly describes the experimental spectra. In Figure 2, the number of constituent functions is six, and the peak wavenumbers (wnIRi and wnRSi) and half-value widths (wIRi and wRSi) for each band in both of the spectra were nearly identical to each other, while the heights (hIRi and hRSi) for each band did not coincide. As described above, a ratio of the value of hIR1 at wIR1 = 1018 cm1 to hIR0 at wIR0 = 953 cm1 is significantly higher than that of hRS1 to hRS0 in the RS spectrum shown in Figure 2b. The values of wnIRi and wnRSi (i g 2) increased and exhibited a blue shift with decreasing c, whereas wnIRi and wnRSi (i = 0 and 1) decreased (i.e., exhibited a red shift). The products of wIRi hIRi mean absorbance (Ai) in the IR spectra for each constituent band. The relative magnitudes of each IR absorption band (Ai‑0 = Ai(A0)1) to A0 quantitatively specifies the relative contribution of each constituent band to the (standard) methyl rocking mode,
’ RESULTS AND DISCUSSION Vibrational Spectroscopic Behavior. 1. DMSO/CCl4 System. The IR and RS spectra for DMSO/CCl4 solutions with the same concentration were similar to each other in a wavenumber or Raman shift ranging from 1000 to 1100 cm1, which primarily involves the SdO stretching vibrations of the DMSO molecules shown in parts a and b of Figure 1. The spectra shown in Figure 1 show the typical variations observed from changing the
Figure 1. (a) Typical IR spectra for a DMSO/CCl4 solution at c = 0.08, 4.0, 14.08 M (pure DMSO) and 25 °C. (b) Typical RS spectra for the DMSO/ CCl4 solution obtained at c = 0.08, 4.4, 14.08 M. 992
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Figure 2. (a) Typical results for the decomposition of the (a) IR and (b) RS spectra for DMSO in the pure liquid state (c = 14.08M) obtained at 25 °C into constituent Lorentz function-type bands (i = 05).
wIR0 = 950 cm1 at c = 14.08 M. The relative magnitudes of modes A20 and A30 decreased as the c decreased, while A40 and A50 increased. These results revealed that modes i = 2 and 3 correspond to the SdO stretching vibrations of DMSO intermolecular dimeric associations fixed in an antiparallel cyclic conformation and that modes i = 4 and 5 correspond to that of monomeric DMSO molecules.4,9 The reason why the SdO stretching vibration mode of the monomeric DMSO molecule split into two bands bearing slightly different wavenumbers, i = 4 and 5, is not clear at present. According to theoretical considerations, if the antiparallel cyclic dimer of DMSO strictly possesses an inverse-symmetry center, then the in-phase SdO stretching vibration is observed only in the RS spectra. However, the out-of-phase stretching is observed only in the IR spectra at a wavenumber different from that of the RS active in-phase band. Fawcett et al.5 assigned the vibrational modes observed at 1042 cm1 in the RS spectra and at 1044 cm1 in the IR spectra for DMSO in the pure liquid state to the in-phase and out-of-phase vibrations, respectively. However, Skripkin et al.9 assigned the vibrational mode found at 1063 cm1 in the IR spectra for DMSO in the pure liquid state to the out-of-phase stretching. If the antiparallel cyclic dimers do not strictly possess the inverse-symmetry center, then the inphase vibration of the SdO is indeed observed in the RS spectra, and the not-in-phase vibrations are observed both in RS and IR spectra. Because the formation of the antiparallel cyclic dimers should consist of a mixture of dimers with and without the inverse-symmetric center, the in-phase and not-in-phase vibrations would be observed in the RS spectra and the out-of-phase and not-in-phase vibrations would be observed in the IR spectra. On the basis of these considerations, the IR bands observed at wnIR2 = 1029 cm1 and wnIR3 = 1047 cm1 for DMSO in the pure liquid state were provably attributed to the not-in-phase and out-of-phase SdO vibrations as proposed by Fawcett et al.,5 respectively. Moreover, the RS bands at wnRS2 = 1028 cm1 and wnRS3 = 1044 cm1 were attributed to the not-in-phase and in-phase vibrations, respectively. However, the reason why two bands are observed for the SdO stretching vibration mode of the antiparallel cyclic dimer is still under controversy. There would be other possible ideas describing the two bands in the IR and RS spectra for the antiparallel cyclic dimer. For example, a difference in the wavenumber of the SdO stretching vibration of DMSO in the dimer possessing a hydrogen bond to a methyl hydrogen of the associating partner and that without the hydrogen bond is possibly a reason for the two bands. The formation of intermolecular dimeric associations of DMSO in the pure liquid state and in solution can be quantitatively
formulated by a chemical equilibrium between the monomeric DMSO molecules (MONs) and the dimeric associations (DIMs) expressed as Rf
ð1Þ
2MON a DIM Rb
where Rf and Rb are the forward and backward rate constants, respectively, when only the formation of DIMs is assumed. The molar fraction of free MONs (fMON = [MON]c1) in the DMSO solution at room temperature, ca. 25 °C, can be discussed using the chemical equilibrium in eq 1. The DIMs dissociate and exchange their partners at a rate governed by an equilibrium constant, Kd [DIM]/[MON]2 (= Rf /Rb). The rate constant of the DIM dissociation, Rb, which is the reciprocal of the average DIM lifetime, should correspond to a longer dielectric relaxation time that is discussed in detail later. From the relationship c = 2[DIM] + [MON], one can calculate [MON] via eq 25 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 1 þ 8cKd ½MON ¼ ð2Þ 4Kd The values of fMON can also be calculated using the equilibrium constant, Kd, and c. By use of the absorbance coefficients (aMON and aDIM) for the MONs and DIMs, the absorbance for these species is described as AMON = aMON[MON] and ADIM = aDIM[DIM], respectively. When the c value is sufficiently low, these absorbance coefficients, aMON and aDIM, should be independent of c. Then, eqs 3 and 4 are obtained. c AMON
¼
1 aMON
þ
2Kd AMON aMON 2
pffiffiffiffiffiffiffiffiffiffi c 1 2 ADIM pffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ aDIM Kd aDIM ADIM
ð3Þ ð4Þ
When the AMON values are calculated exactly, the plot of c(AMON)1 as a function of AMON provides an intercept of aMON1 and a slope of 2Kd(aMON)2, and the plot of c(ADIM)1/2 as a function of ADIM1/2 provides a slope of 2(aDIM)1 and an intercept of (KdaDIM)1/2. The Kd value can be evaluated from the two independent plots. In this study, AMON = A4 + A5, ADIM = A2 + A3, and ADMSO = aDMSOc = A0 for the (standard) methyl-rocking mode, i = 0, is obtained from the vibrational bands attributed to the SdO vibrations in the MONs and DIMs. Moreover, because we only precisely determined the relative magnitudes of the absorbance, AMON‑0 (= AMON(A0)1) and ADIM‑0 (= ADIM(A0)1), a plot of 993
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Figure 3. (a) The relationship between AMON‑01 and cAMON‑0 and (b) the relationship between (cADIM‑01)1/2 and (cADIM‑0)1/2 for data from IR absorption measurements of the DMSO/CCl4 system.
AMON‑01 as a function of ADIM‑0c provided an intercept of aDMSO(aMON)1 and a slope of 2Kd(aDMSO(aMON)1)2, as shown in Figure 3a. In addition, a plot of (cADIM‑01)1/2 as a function of (ADIM‑0 c)1/2 provided a slope of 2aDMSO(aDIM)1 and an intercept of (aDMSO(KdaDIM)1)1/2 (Figure 3b). Consequently, the values of aDMSO(aMON)1, aDMSO(aDIM)1, and Kd were obtained under dilute conditions, as shown in Figure 3. The agreement between the evaluated Kd value from parts a and b of Figure 3 in the low c range is reasonable. This Kd value, ca. 2.5 ( 0.5, for DMSO/CCl4 is greater than that reported by Figueroa et al.3 by a factor more than two due to their erroneous band assignment. Moreover, the Kd value of 0.22 M1 determined by Fawcett et al.5 for DMSO/acetonitrile solutions, which is much lower than 2.0 M1, indicates that a polar solvent, such as acetonitrile, has a stronger ability to dissolve DMSO as individual MONs than CCl4. The assumption that the constant absorption coefficients are independent of c is not reliable over a wide c range. The complicated relationship between (cADIM‑01)1/2 and (c ADIM‑0)1/2 shown in Figure 3b reveals that both the values of aDMSO(aMON)1 and Kd change with c. However, it is expected that the values of aDMSO(aMON)1, aDMSO(aDIM)1, and Kd are less dependent on c as c approaches the pure liquid state (c = 14.08M) because an approximately linear relationship is shown in Figure 3 in the high c range (or high AMON‑0c and (ADIM‑0c)1/2 ranges). The red solid lines in the high c range shown in parts a and b of Figure 3 allowed for the rough estimation of aDMSO(aMON)1 ≈ 0.01, aDMSO(aDIM)1 ≈ 0.1, and Kd = 2040 M1. Consequently, we might conclude that Kd is ca. 2.5 ( 0.5 M 1 in the low c range and increases up to 20 to 40 M 1 in the high c range, which is close to the pure liquid state. The data analysis procedure performed for the IR data was also performed for the RS data, and the results are shown in Figures 4 and 5. The product of wRSi hRSi (Bi) indicates the intensity of the scattered light for each vibrational band in the RS spectra. The c dependencies of the relative intensities of each vibration mode (Bi‑0 = Bi(B0)1) to the standard methyl rocking mode, i = 0, are plotted in Figure 4. In the RS spectra, modes i = 2 and 3 are attributed to the vibrational modes of the SdO stretching in the antiparallel cyclic dimers, and those of i = 4 and 5 are attributed to the SdO stretching vibration modes of the monomeric DMSO molecules. The relationship BMON = B4 + B5 and BDIM = B2 + B3 is obtained. In addition, the proportionality constants (bNOM and bDIM) relating equations BMON = bMON[MON], BDIM = bDIM[DIM], and B0 = bDMSOc were used in the analysis. The values of BMON‑0 (BMON(B0)1) and BDIM‑0 (= BDIM(B0)1)
Figure 4. Dependence of the relative RS intensities for each constituent vibrational band, Bi‑0, to the standard band (i = 0) observed at 950 cm1 on c for the DMSO/CCl4 system.
were used to obtain the c dependence of Kd. A plot of BMON‑01 as a function of BDIM‑0 provided an intercept of bDMSO(bMON)1 and a slope of 2Kd(bDMSO(bMON)1)2, as shown in Figure 5a. In addition, a plot of (cBDIM‑01)1/2 as a function of (cBDIM‑0)1/2 provided a slope of 2bDMSO(bDIM)1 and an intercept of (bDMSO(KdbDIM)1)1/2 (Figure 5b). The conclusions obtained for the c dependence of Kd from the RS spectra were the same as those obtained from the analysis of the IR data (parts a and b of Figure 3; Kd = 2.5 ( 0.5 M1 in the low c range, and Kd = 2040 M1 in the high c range close to the pure liquid state of DMSO). 2. DMSO/Bz System. All of the IR spectra in the range of 9501100 cm1 for the DMSO/Bz solutions were decomposed into Lorentz function-type constituent bands using curve-fitting procedures. However, minor modes, i = 2 and 5, for the SdO stretching vibration bands in the DIMs and MONs were not required to describe the spectra in a c range lower than 0.2 M. Although Bz possesses a relatively strong IR band at 1030 cm1 that is attributed to the in-plane CH bending vibrations, which is close to that of the SdO stretching and methyl rocking modes, the decomposition of the IR spectra into constituent vibrational modes was successful due to the simplicity of the Bz band observed at 1030 cm1 that exhibited a weak wavenumber shift with c. The dependencies of the values of wnIRi and Ai-0 on c are shown in parts a and b of Figure 6 for the system. The values of wnIRi (i g 3) exhibited a blue shift with increasing c, whereas the wnIRi (i e 2) exhibited a red shift. For the DMSO/CCl4 system, the wnIR2 exhibited a blue shift with increasing c (Figure 6a). Figure 6b shows the c dependencies of the relative magnitudes of IR absorption, Ai‑0, to the methyl rocking mode observed at wIR0 = 953 cm1 (c = 14.08 M). The relative magnitudes of A20 and A30 decreased with decreasing c, while those of A40 and A50 increased, as was observed for the DMSO/CCl4 solutions. 994
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Figure 5. (a) The relationship between BMON‑01 and cBMON‑0 and (b) the relationship between (cBDIM‑01)1/2 and (cBDIM‑0)1/2 for data from RS measurements of the DMSO/CCl4 system.
Figure 6. Dependencies of wavenumber, wnIRi, (a) for each constituent IR band on c and the relative magnitude of IR absorption for each band, i = 1 to 5, compared to the standard band (i = 0), AIRi‑0, (b) for the DMSO/Bz system.
Figure 7. (a) The relationship between AMON‑01 and cAMON‑0 and (b) the relationship between (cADIM‑01)1/2 and (cADIM‑0)1/2 for data from IR absorption measurements of the DMSO/Bz system.
The dependence of ADIM‑01 on c ADIM‑0 shown in Figure 7a provides an intercept of aDMSO(aMON)1 and a slope of 2Kd(aDMSO(aMON)1)2 in the low c range for DMSO/Bz solutions. Furthermore, a plot of (c(AMON‑0)1)1/2 as a function of (c AMON‑0)1/2 provides a slope of 2aDMSO(aDIM)1 and an intercept of (aDMSO(Kd aDIM)1)1/2 that is also in the low c range, as shown in Figure 7b. Then, the values of aDMSO(aMON)1, aDMSO(aDIM)1, and Kd were determined to be 0.13, 0.06, and 0.6 ∼ 0.7 M1, respectively, in dilute conditions. The Kd value obtained from parts a and b of Figure 7 agreed reasonably well with each other as expected. This Kd value for the DMSO/Bz system in dilute conditions is significantly smaller than that of the DMSO/CCl4 system evaluated above. This disagreement between the Kd values of the two systems indicates that the ability of Bz to dissolve DMSO is stronger than that of CCl4 even though both Bz and CCl4 are typical nonpolar solvents.
Because general expressions for the changes in the aDMSO(aMON)1 and aDMSO(aDIM)1 as functions of c were not known, the Kd value was not determined as a continuous function of c, except for the low and high c ranges via vibration, IR and RS spectroscopic techniques. Dielectric Behavior. The angular frequency (ω) dependence of the real and imaginary ports (ε0 and ε00 ) of the relative complex electric permittivity for the DMSO/CCl4 and DMSO/Bz systems was determined at 25 °C. Figure 8a shows typical dielectric spectra and ε0 and ε00 as a function of ω for the DMSO/Bz system at several c values and 25 °C. In Figure 8a, the solid lines are a sum of two Debye-type relaxation functions (j = 1 and 2) and ε∞ and are expressed as ε0 ¼ 995
2
Δε
j þ ε∞ ∑ 2τ 2 1 þ ω j j¼1
and
ε00 ¼
2
Δε ωτ
j j ∑ 2τ 2 1 þ ω j j¼1
ð5Þ
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Figure 8. (a) Frequency, ω, dependence of the real and imaginary parts of the dielectric permittivities, ε0 and ε00 , for the DMSO/Bz system at several c values and 25 °C and (b) the ColeCole plots for the DMSO/CCl4 and DMSO/Bz systems at c = 1.1 and 1.0 M, respectively.
Figure 9. (a) The dependence of dielectric parameters, Δε1, Δε2, and ε∞, on c and (b) the dependence of τ1 and τ2 on c for the DMSO/CCl4 and DMSO/Bz systems.
The c dependencies of Δε1 and Δε2 are completely different in both the DMSO/CCl4 and DMSO/Bz systems, as shown in Figure 9a. It appears that Δε1 increases in proportion to c (i.e., Δε1 µ c) in the low c range and exhibits a weaker c dependence in the high c range. In addition, Δε2 increases in proportion to the square of c (i.e., Δε2 µ c2) in the low c range and changes its c dependence to Δε2 µ c in the high c range. The c value where the c dependencies of Δε1 and Δε2 significantly changed depended on the type of solvent species. The relationship between the relaxation times, τ1 and τ2, and c for the two systems is shown in Figure 9b. It appears that both τ1 and τ2 do not significantly depend on the concentration. According to the previous dielectric study on DMSO in the pure liquid state,20 the fast, minor dielectric relaxation mode j = 1 is attributed to the rotational relaxation mode of the individual monomeric DMSO molecules, MONs, in its own liquid or solvent, such as CCl4 or Bz. However, the other slow, major relaxation mode corresponds to a partner exchange process in the dimeric DMSO associations, DIMs, in the antiparallel cyclic conformation. Because the antiparallel cyclic dimer has a small dipole moment, its rotational relaxation time is not detectable by DR techniques. The rate constant of the DIM dissociation, Rb, in eq 1, which is the reciprocal of the average DIM lifetime, corresponds to τ21 because each MON that dissociates from a DIM quickly begins to rapidly rotate with a rate constant close to τ11, which is responsible for the relaxation mode j = 2 bearing an effective dipole smaller than the
which agrees perfectly with the results from previous experiments.20,23 The relaxation times, τ1 and ( 0; the Debye-type relaxation is obtained when β = 1), respectively. Most dielectric spectra in this study did not possess data in a high enough ω range to precisely determine parameters for the DavidsonCole (DC) model in both the DMSO/CCl4 and DMSO/Bz systems, as shown in Figure 8a. The two Debye-type relaxation parameters were used for analysis, and the two relaxation modes were attributed to distinctly different molecular origins as described below. 996
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Scheme 1. A Chemical Equilibrium between Two Monomeric DMSO Molecules, MONs, and a Dimeric Association, DIM, in a Solution of Nonpolar Liquids
Figure 10. (a) The dependence of gk, γMON, and γMON(2γDIM)1 on c and (b) dependencies of fMON and Kd on c for the DMSO/CCl4 and DMSO/Bz systems. The solid and broken lines represent Kd values determined using IR and RS spectroscopic techniques, respectively.
Figure 10a shows the c dependence of the Kirkwood factor, gK, calculated via the equation23
value of |μ| = 3.96 D for a free MON, as schematically depicted in Scheme 1. Consequently, the rate-determining process for the observed dielectric relaxation mode j = 2 is the dissociation of the DIMs. Because the longer dielectric relaxation times, τ2, are related to the lifetime of the dimeric association, DIM, the dependence of τ2 on c shown in Figure 9b indicates that the lifetime of the DIMs formed in CCl4 is longer than the lifetime of the DIMs formed in Bz. This result suggests that the ability of Bz to dissolve DMSO or deconstruct the DIM into MONs is stronger than that of CCl4. In addition, the value of τ1 provides useful information on the molecular size of the MONs. For ordinary polar molecules without molecular associations, the DR time (τd) is described by τd µ Vη(kBT)1, where V, kB, and η represent the effective molecular volume, Boltzmann’s constant, and the viscosity of the liquid, respectively.23 In dilute conditions with c < 1.0 M, the τ1 values corresponding to τd for the MONs were nearly constant values for both the DMSO/CCl4 and DMSO/Bz systems. In such dilute conditions, the η values are not very different from those of CCl4 and Bz in their pure liquid state, 0.91 and (>) 0.61 mPas, respectively.25 However, the τ1 in the DMSO/CCl4 system (ca. 5.0 ps) is almost identical to that in the DMSO/Bz system in the low c range. These results indicate that the effective molecular volume, V, of the MONs in the DMSO/Bz system is slightly larger than that in the DMSO/CCl4 system due to the greater solvation number caused by the stronger dissolving ability of Bz compared to CCl4.
gK ¼
9ðε0 ε∞ Þð2ε0 þ ε∞ Þεv kB T ε0 ðε∞ þ 2Þ2 cNA μ2
ð7Þ
where ε0 = Δε1 + Δε2 + ε∞, |μ| = 3.96 D for gaseous DMSO,26 c represents the molar concentration with units of mol cm3, NA is Avogadro’s number, and εv is the electric permittivity in a vacuum. The relationship gK ≈ 0.5 clearly indicates a pure liquid state, c = 14.08 M, leading to the conclusion that the DMSO dipoles interact in an antiparallel manner, which is completely opposite to the results of many previous dielectric studies.1619 In a few previous dielectric studies, the importance of strong antiparallel interactions of DMSO has been indicated for both the pure liquid state and in solution. For example, Kaatze et al.27 and Lu et al.28 have used measured ε∞ values and obtained a gK ≈ 0.5. The gK values increase with decreasing c and likely approach unity for low c, as shown in Figure 10a, which indicates free rotation of the MONs without any interaction between the dipoles of the dissolved MONs. Because the magnitude of the dielectric relaxation strength should be proportional to the number density of NOMs and DIMs, the formulas Δε1 = γMON[MON] and Δε2 = γDIM[DIM] are obtained with the proportionality constants, γMON and γDIM, for MON and DIM, respectively. For a special test condition where [DIM] = 0, [MON] = c, and gK = 1 for eq 7, the values of 997
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methods corresponded well to each other. A Kd of 2.5 ( 0.5 M1 and 0.7 ( 0.1 M1 was obtained in dilute CCl4 and Bz solutions, respectively, and the value dramatically increased to 20 to 40 M1 in pure DMSO at 25 °C. The DR techniques are highly useful tools that exhibit the potential to investigate the dimerization processes of dipolar molecules, such as DMSO.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was partially supported by KAKENHI: Grant-inAid for Scientific Research on Priority Area “Soft Matter Physics”, KAKENHI: Grant-in-Aid for Scientific Research (B), 2009-2011, A213500640 from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by the Collaborative Research Program of Institute for Chemical Research, Kyoto University (Grant No. 2011-47). ’ REFERENCES (1) Vaisman, I. I.; Berkowitz, M. L. J. Am. Chem. Soc. 1992, 144, 7889–7896. (2) Chalaris, M.; Marinakis, S.; Dellis, D. Fluid Phase Equilib. 2008, 267, 47–60. (3) Figueroa, R. H.; Roig, E.; Szmant, H. H. Spectrochem. Acta 1966, 22, 587–592. (4) Forel, M. -T.; Tranquille, M. Spectrochem. Acta 1970, 26A, 1023– 1034. (5) Fawcett, W. R.; Kloss, A. A. J. Chem. Soc., Faraday Trans. 1996, 92, 3333–3337. (6) Fawcett, W. R.; Kloss, A. A. J. Phys. Chem. 1996, 100, 2019–2024. (7) Fine, G.; Mirone, P. Spectrochem. Acta 1976, 32A, 625–629. (8) Sastry, M. I. S.; Singh, S. J. Raman Spectrosc. 1984, 15, 80–85. (9) Skripkin, M. Y.; Lindqvist-Reis, P.; Abbasi, A.; Mink, J.; Persson, I.; Sandstr€om, M. Dalton Trans. 2004, 4038–4049. (10) Perelygin, I. S.; Itkulov, I. G.; Krauze, A. S. Russ. J. Phys. Chem. 1991, 65, 410–414. (11) Kai, T.; Ueki, K.; Yoshida, K.; Yamaguchi, T. Fukuokadaigaku rigakushuhou 2008, 38, 17–28. (12) McLain, S. E.; Soper, A. K.; Kuzar, A. J. Chem. Phys. 2006, 124, 074502–112. (13) Tori, H.; Tatsumi, M. Bull. Chem. Soc. Jpn. 1995, 68, 128–134. (14) Rao, B. G.; Singh, U. C. J. Am. Chem. Soc. 1990, 112, 3803– 3811. (15) Gajada, R.; Katrusiak, A. J. Phys. Chem. B 2009, 113, 2436– 3442. (16) Amey, R. L. J. Phys. Chem. 1968, 72, 3358–3359. (17) Gabrielian, L. S.; Markarian, S. A. J. Mol. Liq. 2004, 112, 137–140. (18) Hunger, J.; Buchner, R.; Kandil, M. E.; Marsh, K. N. J. Chem. Eng. Data 2010, 55, 2055–2065. (19) Prestbo, E. W.; McHale, J. L. J. Chem. Eng. Data 1984, 29, 387–389. (20) Shikata, T.; Sugimoto, N. Phys. Chem. Chem. Phys. 2011, 13, 16542–16547. (21) Stokes, R. H. J. Chem. Thermodynamics 1973, 5, 379–385. (22) Brown, A. S.; Levin, P. M.; Abrahamson, E. W. J. Chem. Phys. 1951, 19, 1226–1229. (23) Fr€ohlich, H. Theory of Dielectrics; Oxford Univ. Press: Oxford, 1959. (24) Davidson, D. W.; Cole, R. H. J. Chem. Phys. 1951, 18, 1417– 1417.
’ CONCLUSIONS DMSO forms intermolecular dimeric associations with an antiparallel cyclic configuration in both the pure liquid state and in nonpolar solvents, such as CCl4 and Bz. The dimerization process of DMSO was well described by a chemical reaction, and the equilibrium constant, Kd, was determined as function of c using conventional vibrational spectroscopic methods, such as IR and RS techniques as well as DR measurements in the highfrequency range up to 50 GHz. Although the vibrational spectroscopic methods allowed for the determination of the Kd value in the limited low and high c range, the DR techniques provided a Kd value over the entire c range that was examined. The Kd values and the related parameters determined using these independent 998
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(25) CRC Hand Book of Chemistry and Physics, 85th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2004, (26) Driezler, H.; Dendl, G. Z. Naturforsch. 1964, 19A, 512–514. (27) Kaatze, U.; Pottel, R.; Schafer, M. J. Phys. Chem. 1989, 93, 5623–5627. (28) Lu, Z.; Manias, E.; Macdonald, D. D.; Lanagan, M. J. Phys. Chem. A 2009, 113, 12207–12214.
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